The growth of the range of stable random walks

Wojciech Cygan, Nikola Sandrić, Stjepan Sebek

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this article, we establish an almost sure invariance principle for the capacity
and cardinality of the range for a class of α-stable random walks on the integer
lattice Zd with d > 5α/2 and d > 3α/2, respectively. As a direct consequence, we
conclude Khintchine's and Chung's laws of the iterated logarithm for both processes.
Original languageEnglish
Number of pages16
JournalarXiv.org e-Print archive
Publication statusSubmitted - 2019

Fingerprint

Almost Sure Invariance Principle
Law of the Iterated Logarithm
Cardinality
Random walk
Range of data
Class

Keywords

  • The range of a random walk
  • Capacity
  • An almost sure invariance principle
  • The law of the iterated logarithm

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cygan, W., Sandrić, N., & Sebek, S. (2019). The growth of the range of stable random walks. Manuscript submitted for publication.

The growth of the range of stable random walks. / Cygan, Wojciech; Sandrić, Nikola; Sebek, Stjepan.

In: arXiv.org e-Print archive, 2019.

Research output: Contribution to journalArticleResearchpeer-review

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